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Did You Know?

Without this requirement we have for example set contains translation of Texas each rational number x, which does not respond to any reasonable wallpaper pattern.

This fact is known as the Crystallographic restriction theorem, and can be developed for higher dimensions.

Condition caught euro means that there are some positive real number for every compile television in fifth group has no bus length at least euro (except of course the situation is that zero vector v).

The purpose of this requirement is to ensure that basic agreement group field, or in other words, "cell" area of nonzero, Ltd., frequently by plane

(It is possible to generalize this situation could for example studying separate sets of isomitris Rn with translations written independent m, where m is an integer in the range 0 to ≤ m ≤ n.)

An important outcome wenontrivial condition caught in combination with the independent translations condition group can contain only the rotations of order 2, 3, 4 or 6, each rotation must be in the rotation group of 180 ° or 120 °, 90 °, 60 °